Some Characterizations of GVNL Rings

A ring R is called a GVNL-ring if a or 1 - a is π-regular for every a ∈ R,as a common generalization of local and π-regular rings.It is proved that if R is a GVNL ring,then either (1 -e)R( 1 -e) or eRe is a π-regular ring for every idempotent e of R.We prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is SGVNL.The formal power series ring Rx] is GVNL if and only if R is a local ring.